eureka math™ tips for parents - issaquah.wednet.edu

Eureka Math™ Tips for Parents

Prepared by Erin Schweng, Math Coach

Grade 5 Module 1

+ • Understand the place value system

o Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left

o Explain patterns in the number of zeros of the product when multiplying whole numbers by powers of 10

o Read, write, and compare decimals to thousandths o Use place value understanding to round decimals to any place

• Perform operations with multi-digit whole numbers and with

decimals to hundredths o Add, subtract, multiply, and divide decimals to hundredths

• Convert like measurement units within a given measurement

system o Convert among different-sized standard measurement units within a

given measurement system

Key Common Core Standards:

Place Value and Decimal Fractions

How you can help at home:

• When given a multi-digit number with decimal digits, ask your student what each digit represents (e.g., “What is the value of the 4 in the number 37.346?”)

• Help practice writing numbers correctly by saying multi-digit decimal numbers and having your student write them down. Students can create their own place value charts to help

•

In this first module of Grade 5, we will extend 4th grade place value work to multi-digit numbers with decimals to the thousandths place. Students will learn the pattern that one-tenth times any digit on the place value chart moves it one place value to the right. They will also perform decimal operations to the hundredths place.

Terms, Phrases, and Strategies in this Module: Thousandths: related to place value (we have already studied tenths and hundredths) Exponents: how many times a number is to be used in a multiplication sentence Millimeter: a metric unit of length equal to one thousandth of a meter Equation: statement that two mathematical expressions have the same value, indicated by use of the symbol =; e.g., 12 = 4 x 2 + 4 Place value: the numerical value that a digit has by virtue of its position in a number Standard form: a number written in the format: 135 Expanded form: e.g., 100 + 30 + 5 = 135 Unit form: e.g., 3.21 = 3 ones 2 tenths 1 hundredth Word form: e.g., one hundred thirty-five

What Comes After this Module: In Module 2, we will continue to work with place value, moving to multiplication and division of decimal numbers. We move from concrete models to more abstract algorithms, always anchoring our work in our knowledge of place value patterns.

0.2 x 3 on the place value chart.

Notice how the dots for two tenths are simply repeated three times for

a total of 0.6, or six tenths.

Place value chart for comparing decimals using <, >, =

Grade 5 Module 1Eureka Math, A Story of Units

Read on to learn a little bit about Eureka Math, the creators of A Story of Units:

Eureka Math is a complete, PreK–12 curriculum and professional development platform. It follows the focus and coherence of the Common Core State Standards (CCSS) and carefully sequences the progression of mathematical ideas into expertly crafted instructional modules.

This curriculum is distinguished not only by its adherence to the CCSS; it is also based on a theory of teaching math that is proven to work. That theory posits that mathematical knowledge is conveyed most effectively when it is taught in a sequence that follows the “story” of mathematics itself. This is why we call the elementary portion of Eureka Math "A Story of Units." The sequencing has been joined with methods of instruction that have been proven to work, in this nation and abroad. These methods drive student understanding beyond process, to deep mastery of mathematical concepts.

The goal of Eureka Math is to produce students who are not merely literate, but fluent, in mathematics. Your student has an exciting year of discovering the story of mathematics ahead!

Sample Problem from Module 1: (Example taken from Module 1, Lesson 10)

Teacher says:

“Subtract 2 ones 3 thousandths from 7 ones 5 thousandths.”

Students use place value chart to solve.

Place Value Chart – In Module 1, students will make extensive use of place value tools, as they have done in earlier grade levels. Now, however, students work with the extended place value chart, which includes place values to the thousandths.

(Above) Place Value Chart, with the thousandths place

(Below) 27.346 on the chart

Welcome to A Story of Units!

Each module’s parent tip sheet will highlight a new strategy or math model your student will be working on.

From the non-profit Great MindsFor more information visit greatminds.net


+ • Write and interpret numerical expressions, e.g., “Add

8 and 7, then multiply by 2” is represented as 2 x (8 + 7)


Multiplying and Dividing Whole Numbers and Decimals

How you can help at home:

• Become familiar with the area model, a different method of multiplying than you may have learned

• Continue to review the place value system with your student

• Discuss mathematical patterns, such as 5 x 9, 5 x 90, 50 x 90, 50 x 900, etc.

In this module, we will be building up our knowledge of first multiplication and then division. We will start with whole numbers and then move to decimals as we practice different ways to model these operations.

Key Words to Know

Decimal: A fraction whose denominator is a power of ten Decimal Fraction: A proper fraction whose denominator is a power of ten

Estimate: Approximation of the value of a quantity or number Product: The result of a multiplication Quotient: The result of dividing one quantity by another

What Came Before this Module: We worked very hard to understand the values of numbers on the place value chart.

What Comes After this Module: We will begin work with the base-10 place value system

Equation: A statement that the values of two expressions are equal

• Perform operations with multi-digit whole numbers and with decimals to the hundredths, e.g., 46 x 72, 3.1 x 33

Sample area model of multiplication for 64 x 73:

Thinking mathematically is hard but important work!

• Convert like measurement units within a given measurement system, e.g., 5 cm is 0.05 m

Remainder: The number left over when one integer is divided by another Unit Form: Place value counting, e.g., 34 is stated as 3 tens 4 ones

Grade 5 Module 2 Eureka Math™ Tips for Parents

Eureka Math, A Story of Units

The tape diagram is a powerful model that students can use to solve various kinds

of problems. In second grade, you will often see this model as an aid to addition and

subtraction problems. Tape diagrams are also called “bar models” and consist of a

simple bar drawing that students make and adjust to fit a word problem. They then

use the drawing to discuss and solve the problem.

As students move through the grades, tape diagrams provide an essential bridge to

algebra. Below is a sample word problem from Module 2 solved using a tape diagram to show the parts of the problem.

Sample Problem from Module 2: (Example taken from Lesson 3, Module 2)

Robin is 11 years old. Her mother, Gwen, is 2 years more than 3 times Robin’s age. How old is Gwen?

A Story of Units has several key mathematical “models” that will be used throughout a student’s elementary years.

Spotlight on Math Models:

Tape Diagrams

You will often see this mathematical representation in A Story of Units.

Grade 5 Module 2



+

1

Use equivalent fractions as a strategy to add and

subtract fractions

o Add and subtract fractions with unlike denominators

o Solve word problems involving addition and

subtraction of fractions


Addition and Subtraction of Fractions

How you can

help at home:

Look for opportunities in

daily life to discuss

fractional parts of a

whole, e.g. pieces of

pizza, parts of an hour,

distances to familiar

places

Continue to practice and

review multiplication

and division math facts –

this greatly supports

work with fractions!

In this 16-lesson unit, students build on earlier work with equivalent fractions and decimals to add and subtract fractions with unlike denominators. They will move from concrete examples (paper strips and number lines) to abstract skills (writing their own math sentences). By the end of the module, students will fluently work through multi-step word problems that contextualize

their learning.

Key Words:

What Came Before this Module: We worked to build

our knowledge of multiplication and division of whole numbers and decimals.

What Comes After this Module: In Module 4, we will

extend our understanding of fraction operations to multiplication and division of both fractions and decimal fractions.

Denominator – shows the fractional unit, e.g. the fifths in 3 fifths

Numerator – shows how many fractional units there are, e.g. the 3 in 3 fifths

Benchmark Fraction – a very familiar fraction that can be referred to in comparison

questions, e.g. is a

benchmark fraction used when

comparing and

Like Denominators – fractions with the same denominator,

e.g. and

Unlike Denominators – fractions with different

denominators, e.g. and

Equivalent Fraction – fractions that have the same value, though they may look

different, e.g. and

Fraction Greater than or

equal to 1 – e.g. or 2

Both the area model and number line show the equivalent fractions

of and .

Grade 5 Module 3

Subtraction with unlike denominators:


Eureka Math, A Story of Units

Students began in earlier grades to build arrays for various purposes, first showing

simple multiplication. In 5th grade, we move beyond using the area model for

multiplication of whole numbers and begin to use this powerful model to illustrate

mathematical operations on fractions.

One of the goals in A Story of Units is to first give students concrete experiences

with mathematical concepts, and then to build slowly toward more abstract

representations of those concepts. The area model is a tool that helps students to

make that important leap, and will support students’ learning through algebra and

beyond.

Sample Problem from Module 3: (Example taken from Lesson 7)

Jing spent of her money on a pack

of pens, of her money on a pack

of markers, and of her money on

a pack of pencils.

What fraction of her money is left?


Spotlight on Math

Models:

Area Models

You will often see

this mathematical

representation in A

Story of Units.

Grade 5 Module 3

Below is an area model drawing of –

. Note that the final answer would

be found by doing the simple

subtraction problem:

.

Above is an area model drawing

of + . Note that the final answer

would be found by doing the

simple addition problem:

The student here has illustrated the

equivalent fractions to , , and ,

using the like denominator of

twenty-fourths.

Then, in two steps, she adds those

equivalent fractions, and subtracts

that total from to find the

solution.



+

Grade 5 Module 4

Write and interpret numerical expressions.

Perform operations with multi-digit whole

numbers and with decimals to hundredths.

Apply and extend previous understandings of

multiplication and division to multiply and divide

fractions.

Convert like measurement units within a given

measurement system.

Represent and interpret data.


Multiplication and Division of Fractions and Decimal

Fractions

How you can

help at home:

Continue to practice

and review

multiplication and

division math facts –

this greatly supports

work with fractions!

Look for opportunities

in daily life to discuss

both fractional parts of

a whole and of other

fractions, e.g. What is

¼ of 20? ¼ of ½?

In this 38-day module, students learn to multiply fractions and decimal fractions and start work with fraction division. Students will begin by measuring fractional parts on a number line as a concrete way of understanding fractional parts of a whole, and eventually move to more abstract fraction operations.

New Terms in this Module:

Decimal divisor- the number that divides the whole and that has units of tenths, hundredths, thousandths, e.g. 1/100

Simplify - using the largest fractional unit possible to express an equivalent fraction, e.g. 4/6 simplifies to 2/3, withthe denominator 3 being a larger fractional unit than 6

Familiar Terms with Some Definitions:

Denominator

Decimal Fraction

Equation

Equivalent Fraction

Factors - numbers that aremultiplied to obtain a product

Line Plot

Mixed Number

Numerator

Tape Diagram

Unit - one segment of apartitioned tape diagram

Unknown - the missing factoror quantity in multiplication ordivision

Whole Unit - any unit that ispartitioned into smaller,

equally sized fractional units

What Came Before this Module: We learned to add and

subtract fractions with unlike denominators, moving from

concrete to abstract examples.

What Comes After this Module: In Module 5, we will

work with the area and volume of two- and three-dimensional

figures.

4 3, shown as a traditional algorithm division problem:

A diagram of 4 3 showing fractional division:


Grade 5

Module 4Eureka Math, A Story of Units

Various types of number lines:

A ruler number line

Note the use of a tape diagram as well as the drawing showing division of a whole number into fractional parts:

The number line is a powerful, flexible model that students can use in many ways.

In this particular module, students begin to understand the idea of fractions as division

by marking a ruler or line plot with 1

2,

1

4, and

1

8 increments.

The number line is used beginning in Kindergarten in A Story of Units, and will

continue to appear in various forms through 5th grade. It is used to develop a deeper

understanding of whole number units, fraction units, measurement units, decimals, and

negative numbers. Often, the mathematical concepts in an ASOU module move from

concrete to more abstract, and the number line is an important concrete conceptual

step for students of all ages.

Sample Problem from Module 4: (Example taken from Lesson 5)

Forty students shared 5 pizzas equally. How much pizza did each student receive?

What fraction of the pizza did each student receive?

A Story of Units has several key mathematical “models” that

will be used throughout a student’s elementary years.

Spotlight on Math

Models:

Number Lines

You will often see

this mathematical

representation in

A Story of Units.

The clock – a circular number line!



Eureka Math™ Tips for Parents Grade 5

Module 5

+ Key Common Core Standards: Apply and extend previous understanding of multiplication and

division to multiply and divide fractions.o Multiply a fraction or whole number by a fraction.o Solve real world problems involving multiplication of

fractions and mixed numbers.

Geometric measurement: understand concepts of volume andrelate volume to multiplication and addition.

o Recognize volume as an attribute of solid figures andunderstand concepts of volume measurement.

o Measure volumes by counting unit cubes of various units.o Relate volume to the operations of multiplication and

addition.

Classify two-dimensional figures into categories based on theirproperties.

o Understand that attributes belonging to a category of figuresalso belong to all subcategories of that category.

Addition and Multiplication

with Volume and Area

How You Can

Help at Home:

Begin to discuss and

notice the volume of

various household

containers—this is also

a good opportunity to

talk about what units

are often used to

measure volume.

Keep practicing those

multiplication and

division facts,

especially as problems

become more complex.

In Module 6, students begin by reasoning about and working with three-dimensional shapes. They explore cubic units and move toward calculations of volumes of rectangular prisms. Students also extend their two-dimensional work with area to figures with fractional side lengths. This module bridges the Grade 4 work on area with the Grade 6 work on volume and area to

come.


Base: one face of a three-dimensional solid—often thought of as the surface upon which the solid rests

Bisect: divide into two equal parts

Cubic units: cubes of the same size used for measuring

Height: adjacent layers of the base that form a rectangular prism

Hierarchy: series of ordered groupings of shapes

Unit cube: cube whose sides all measure 1 unit

Volume of a solid: measurement of space or capacity

What Came Before this Module: Students learned to

multiply fractions and decimal fractions and began work on fraction division, working from concrete to

abstract representations.

What Comes After this Module: In Module 6, students

begin to explore the coordinate plane, working from the familiar number line toward plotting points and creating lines and patterns.

Two orientations of 12 unit cubes

Unit Cubes An area calculation for 3½ × 1¼

Eureka Math, A Story of Units Grade 5

Module 5

Earlier in Grade 5, we moved beyond using the area model for multiplication of

whole numbers and begin to use this powerful model to illustrate mathematical

operations on fractions. Now, we move a step further and use the area model in

various real world problems, e.g., finding the area of a wall minus the space for two

windows, or finding the area of a mat surrounding a picture in a frame.

The numbers we use in our area models now are often mixed whole numbers and

fractions, giving students a chance to demonstrate their understanding in diagrams in

which they show the multiplication of both the whole number and fractional parts of

the problem.

Sample Volume Problem from Module 5: (Example taken from Module 5, Lesson 18)

How many 2-inch cubes are needed to build a rectangular prism that measures 10 inches by 6 inches by 14 inches?


Spotlight on Math

Models:

Area Model with

Fractional Parts

We will revisit this

mathematical

representation in

Module 5 of A Story

of Units.

Note that the student here shows two ways to solve the problem!

Note that in the area problem above, the numbers are first decomposed and drawn as whole number and fractional parts, and then they are multiplied: 1 × 3, 1/3 × 3, 1 × 3/4, 1/3 × 3/4. Each of these products is then added together to find the total area of the rectangle.



Eureka Math™ Tips for Parents Grade 5

Module 6

+ Key Common Core Standards: Write and interpret numerical expressions.

o Write simple expressions that record calculations with numbers,and interpret numerical expressions.

Analyze patterns and relationships.o Generate two numerical patterns using two given rules, and

identify apparent relationships between corresponding terms.

Graph points on the coordinate plane to solve real-world andmathematical problems.

o Use a pair of perpendicular number lines, called axes, to definea coordinate system.

o Represent real world and mathematical problems by graphingpoints in the first quadrant of the coordinate plane, andinterpret coordinate values of points in the context of thesituation.

Problem Solving with the

Coordinate Plane

How You Can

Help at Home:

Play the game

Battleship, if you have

it! It gives good

practice with locating

points on a coordinate

plane.

Practice following rules

to find ordered pairs,

e.g. if the rule is

y = double x plus 1,

what is y if x is 3? 4?

5? (Answers are

7, 9, 11.)

In Module 6, students develop a coordinate system for the first quadrant of the coordinate plane and use it to solve problems. They explore the relationship between points, ordered pairs, patterns, and lines. The module finishes with an exploration of the coordinate plane in real world

applications.


Axis: fixed reference line for the measurement of coordinates

Coordinate: number that identifies a point on a plane

Coordinate pair: two numbers that are used to identify a point on a plane; written (x, y) where x represents a distance from 0 on the x-axis and y represents a distance from 0 on the y-axis

Coordinate plane: plane spanned by the x-axis and y-axis in which the coordinates of a point are distances from the two perpendicular axes

Ordered pair: two quantities written in a given fixed order, usually written as (x, y)

Origin: fixed point from which coordinates are measured; the point at which the x-axis and y-axis intersect

Quadrant: any of the four equal areas created by dividing

a plane by an x-axis and y-axis

What Came Before this Module: Students worked with three-dimensional shapes and explored cubic units and volumes of rectangular prisms. They also calculated area for figures with fractional side lengths.

The coordinate plane

Drawing figures on the coordinate plane

Eureka Math, A Story of Units Grade 5

Module 6

Module 6, the final module of Grade 5, is a very important link to the algebraic skills

students will need in later years. Students begin by investigating patterns, relating the

x- and y-coordinates of the points on the line and reasoning about the patterns in the ordered

pairs, which lays groundwork for Grade 6 work with proportional reasoning.

Students use given rules (e.g., “multiply by 2, then add 3”) to generate coordinate pairs,

plot points, and investigate relationships. Finally, students generate two number patterns

from two given rules, plot the points, and analyze the relationships within the sequences of

the ordered pairs and the graphs of the two lines.

Sample Problem from Module 6: (Example taken from Module 6, Lesson 20)

Harry runs a hot dog stand at the county fair. When he arrived on Wednesday, he had 38 dozen hot dogs on his stand. The graph shows the number of hot dogs (in dozens) that remained unsold at the end of each day of sales.

1. How many dozen hot dogs did Harry sell onWednesday? How do you know?

2. Between which two-day period did the number ofhot dogs sold change the most? Explain how youdetermined your answer.

A Story of Units teaches students key mathematical skills that will be used throughout a student’s elementary years and beyond.

Spotlight on Math

Skills:

Graphing Lines

Students learn this

important skill in

Module 6 of A Story

of Units.

The rule table and the plotted points for the rule “Double x, then subtract 1”


eureka math™ tips for parents - issaquah.wednet.edu

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